Problem: Simplify; express your answer in exponential form. Assume $p\neq 0, x\neq 0$. $\dfrac{{(p^{3})^{2}}}{{(px^{-5})^{-2}}}$
Answer: To start, try working on the numerator and the denominator independently. In the numerator, we have ${p^{3}}$ to the exponent ${2}$ . Now ${3 \times 2 = 6}$ , so ${(p^{3})^{2} = p^{6}}$ In the denominator, we can use the distributive property of exponents. ${(px^{-5})^{-2} = (p)^{-2}(x^{-5})^{-2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(p^{3})^{2}}}{{(px^{-5})^{-2}}} = \dfrac{{p^{6}}}{{p^{-2}x^{10}}}$ Break up the equation by variable and simplify. $\dfrac{{p^{6}}}{{p^{-2}x^{10}}} = \dfrac{{p^{6}}}{{p^{-2}}} \cdot \dfrac{{1}}{{x^{10}}} = p^{{6} - {(-2)}} \cdot x^{- {10}} = p^{8}x^{-10}$.